A space-indexed formulation of packing boxes into a larger box

Citation

Allen SD, Burke E & Maracek J (2012) A space-indexed formulation of packing boxes into a larger box. Operations Research Letters, 40 (1), pp. 20-24. https://doi.org/10.1016/j.orl.2011.10.008

Abstract
Current integer programming solvers fail to decide whether 12 unit cubes can be packed into a 1×1×11 box within an hour using the natural relaxation of Chen/Padberg. We present an alternative relaxation of the problem of packing boxes into a larger box, which makes it possible to solve much larger instances.

Keywords
Integer programming; Linear programming; Packing; Load planning; Pigeon hole principle

Journal
Operations Research Letters: Volume 40, Issue 1